匿名
匿名 發問於 科學及數學數學 · 6 年前

Finite Math Question

Two people are chosen at random from a group of eight people consisting of 4

married couples. What is the probability that the two people chosen are not married to each other?

A. (8 choose 6) / (8 choose 2)

B. (8 choose 2) / ( 8 choose 4)

C. 1/7

D. 1/4

E. 6/7

2 個解答

評分
  • 6 年前
    最愛解答

    Method 1

    No matter who is chosen as the first one, in the remaining 7 people, 1 of them is married to the first chosen person and 6 of them is not married to the first chosen person.

    Therefore, the required probability

    = Pr(the two people chosen are not married to each other)

    = 6/7 (E)

    Method 2

    Denote:

    Couple 1 = {Husband 1, Wife 1} = {H1, W1}

    Couple 2 = {Husband 2, Wife 2} = {H2, W2}

    Couple 3 = {Husband 3, Wife 3} = {H3, W3}

    Couple 4 = {Husband 4, Wife 4} = {H4, W4}

    If two people chosen are not married to each other, they must be from different couples, then first choose 2 couples out of 4, i.e., (4 choose 2).

    For each of the two chosen couples, choose 1 member from either husband or wife, i.e., (2 choose 1).

    The total number of ways to choose 2 out of 8 is (8 choose 2).

    Therefore, the required probability

    = Pr(the two people chosen are not married to each other)

    = (4 choose 2) (2 choose 1) (2 choose 1) / (8 choose 2)

    = (6 × 2 × 2) / 28

    = 6/7 (E)

    2014-11-06 08:33:25 補充:

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    ╰/) ⋈ (\╯

  • kc
    Lv 7
    6 年前

    我認為功課還是自己做的好.

    希望不要有人為了好心幫人, 而淪為別人的鎗手.

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